Homework Help is Here – Start Your Trial Now!
Math
Statistics
Let X₁,..., Xn be a random sample of size n from the U(0, 0) distribution, where > 0 is an unknown parameter. Recall that the pdf fof the U(0, 0) distribution is of the form 0-¹ if 0

Let X₁,..., Xn be a random sample of size n from the U(0, 0) distribution, where > 0 is an unknown parameter. Recall that the pdf fof the U(0, 0) distribution is of the form 0-¹ if 0

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.CR: Chapter 2 Review
Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...
See similar textbooks
icon
Related questions
Question
Let X₁, Xn be a random sample of size n from the U(0, 0) distribution, where @ > 0 is an unknown parameter. Recall that the pdf fof the U(0, 0) distribution is of the form f(x) = { 0 Note that the information about contained in the random sample X₁, ...,. information about contained in the statistic if 0<x<0 otherwise. T - max(X₁,..., Xn). manner, To understand why so, let's think of the random sample as being obtained in a sequential that is, you obtain X₁ and pause before obtaining X₂. What does X₁ tell you about 0? It tells you that 0 > X₁. Once you have X₁ and the information that > X₁, obtain X₂. If X2 > X₁, then you know a bit more about 9, namely, 0 > X₂; however, if X2X₁, then it does not contribute anything, above and beyond what you already know from X₁, to your knowledge about 0. In other words, when you have obtained X₁ and X2, what you know about is that it is greater than the maximum of X₁ and X₂. As such, any reasonable estimator of 0 should be a function of T. Xn equals the (a) Carefully argue that T is the maximum likelihood estimator of 0. Recall that the likelihood function L of 0, given a data sample ₁,, n, is the product of f(x₁), · ·., f (xn). (b) Construct an unbiased estimator of 0 which is not a function of T and calculate its variance. To start with, you may like to calculate the expected value and the variance of the U(0, 0) distribution.
Transcribed Image Text:Let X₁, Xn be a random sample of size n from the U(0, 0) distribution, where @ > 0 is an unknown parameter. Recall that the pdf fof the U(0, 0) distribution is of the form f(x) = { 0 Note that the information about contained in the random sample X₁, ...,. information about contained in the statistic if 0<x<0 otherwise. T - max(X₁,..., Xn). manner, To understand why so, let's think of the random sample as being obtained in a sequential that is, you obtain X₁ and pause before obtaining X₂. What does X₁ tell you about 0? It tells you that 0 > X₁. Once you have X₁ and the information that > X₁, obtain X₂. If X2 > X₁, then you know a bit more about 9, namely, 0 > X₂; however, if X2X₁, then it does not contribute anything, above and beyond what you already know from X₁, to your knowledge about 0. In other words, when you have obtained X₁ and X2, what you know about is that it is greater than the maximum of X₁ and X₂. As such, any reasonable estimator of 0 should be a function of T. Xn equals the (a) Carefully argue that T is the maximum likelihood estimator of 0. Recall that the likelihood function L of 0, given a data sample ₁,, n, is the product of f(x₁), · ·., f (xn). (b) Construct an unbiased estimator of 0 which is not a function of T and calculate its variance. To start with, you may like to calculate the expected value and the variance of the U(0, 0) distribution.
Expert Solution
steps

Step by step

Solved in 4 steps with 25 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS